Scattering amplitudes in QFT with Poincaré symmetry are multi-linear in the
state vectors of the external particles, i.e., proportional to the tensor product
of all external polarization vectors, to all loop orders in perturbative calculations,
as manifestly shown by the Feynman diagram representations.
The color structure of QCD amplitudes can be conveniently described using
the color-decomposition [1]}, [2]}, [3]}, [4]}, [5]}
or the color-space formalism of ref. [6]}.
QCD amplitudes are thus viewed as abstract vectors in the color space of external colored particles.
Since projecting QCD amplitudes onto the factorized color space and spin (Lorentz) structures
can be done independently of each other, we suppress for ease of notation possible color
indices of scattering amplitudes in the following discussions.
